In many respects, immigration to the United States today is quite unlike that of the early 20th century, when it was overwhelmingly legal, documented, lightly regulated and European in origin. Millions of newcomers then were readily absorbed into a prosperous economy, and the main objection was not that the system was broken but that it was working too well at filling American cities and workplaces with foreigners of unfamiliar tongues and customs.

Immigration debates from the Ellis Island era nonetheless have a familiar ring today. Both sides then praised immigration as an American tradition while disagreeing as to whether newer arrivals were somehow fundamentally less desirable than those of yore.

Both political parties sought immigrant votes, but the Republicans had the harder and more significant circle to square. Their politically stronger party was also the political and intellectual home of the immigration restriction movement, whose leader, Sen. Henry Cabot Lodge of Massachusetts, was a friend of Theodore Roosevelt, the popular U.S. president from 1901 to 1909. A literacy test for incoming immigrants, long advocated by Lodge and a key step toward drastic wholesale immigration restriction, finally passed and survived President Wilson’s veto to become law in 1917.

But several previous attempts at adopting such a test were defeated in the years before World War I — a turning point for immigration policy — largely because the Republican Party as a whole would not risk sacrificing immigrant votes by enacting it.

Roosevelt’s own calculated ambivalence — “We cannot have too much immigration of the right sort, and we should have none whatever of the wrong sort” — placated both pro-immigration and anti-immigration voices, partly because it was accompanied by beefed-up, yet relatively noncontroversial, border monitoring and inspections.

The Republican Party of the early 20th century was ambitious and successful. It was a kind of Progressive Era “Party of Yes.” Yes to overseas colonies, yes to the Panama Canal, yes to capitalist growth, yes to modern financial and monetary policy tools, and yes to international disarmament, consumer protection, trust-busting and conservation.

Being both pro- and anti-immigration — by publicly backing legislation to mandate a literacy test, in 1896, 1906, 1912 and 1914, only to later quietly compromise it away or withdraw support — required deft political maneuvering. But the party’s general popularity was not at stake.

Today’s Republican Party has no comparable roster of recent achievement to which inconsistency on immigration policy might become a comparatively inconspicuous footnote. Being pro-immigration a century ago required only periodic tactical backing off from fairly radical proposed alterations to a clearly functioning and mostly “open border” status quo.

Today, it means ratifying the de facto failure of existing immigration policy and hoping that a revised version of it will work better going forward. It was easier for Roosevelt’s “Party of Yes” to occasionally say no than it will be for House Speaker John A. Boehner’s “Party of No” to make an exception and say yes.

Page 2 of 2 - Last week the Senate passed a comprehensive overhaul immigration bill with a two-thirds vote, but only a “minority of the minority” (the Republicans) supported it. Passage of a compatible bill by the Republican-controlled House of Representatives is far from assured — in fact, many consider it a long shot. There, a “majority of the majority” seem to be reluctant, so far, if not strongly opposed.

In 1906, when the divergence between the House and Senate was the opposite to that of today, pro-immigration Republicans in the House, working through the Republican administration of President Roosevelt, were eventually able to offer substantive yet not crippling concessions that secured support from enough restrictionist Republicans in the Senate to pass a mostly pro-immigration bill.

Is it a stretch to expect that such an internal Republican compromise on a generally pro-immigration bill can be reached in the current Congress, and with a Democrat in the White House?

Many members of Congress are caught up in a short-term re-election calculus that is out of sync with their party’s long-term demographic calculus. Nonetheless, among crucial Republican swing votes on Capitol Hill, there are strong incentives for hammering out a political bargain (conditional amnesty for those here illegally in return for tighter future controls).

During President George W. Bush’s second term, congressional Republicans failed to rally enough party support for bipartisan immigration reform, with the result that its proponents have since formed a more determined political coalition. If Republicans reject immigration reform again, the party risks being blamed for scuttling a rare opportunity for a “do-nothing” Congress to accomplish something noteworthy.

Both political parties realize that now, as a century ago, a little expediency sometimes goes a long way. We have heard a lot about gridlock lately, but the political moment is starting to look opportune for a comeback of strange bedfellows.

Drew Keeling, a historian of international migration and transportation, is the author of “The Business of Transatlantic Migration between Europe and the United States, 1900-1914.” He wrote this for the Los Angeles Times.